Interference between different kinds of particles

I have only an completed one course on quantum mechanics so please excuse me if this seems rudimentary.

In my course we only dealt with electrons and their interference with one another. Is it possible for an electron and a proton to interfere with one another? Or more generally, can different types of particles interfere with each other?

Okay. But the wave functions can still influence each other right? If I were to shoot a proton and neutron at each other and measured the momentum on the proton, assuming I knew the initial momentums, I would be able to figure out the momentum of the neutron in theory. Which means that the wave functions are in an entangled state correct?

Okay. But the wave functions can still influence each other right? If I were to shoot a proton and neutron at each other and measured the momentum on the proton, assuming I knew the initial momentums, I would be able to figure out the momentum of the neutron in theory. Which means that the wave functions are in an entangled state correct?

Yes, that's of course correct. If there is an interaction between particles then that will obviously infuence the time evolution of their wave functions.

No. Only identical particles can interfere - you have to be able to add amplitudes.

We can kinda have interference pattern of different particles, at least in theory.

First we get a particle that decays into few others. Say, a neutron decaying into proton, electron and a neutrino. We shoot this neutron and wait. We can say that it is composed of 3 waves of different speeds. When they all are in phase, we have high probability of detecting a neutron. When the time passes and the 3 waves phase out, we have high probability of detecting proton, electron and neutrino. If we wait a bit longer, the waves will eventually reach the same phase again and create a neutron. I'm assuming that all particles move only in one dimension, but it's only a theory.

If we place detectors along the path of this particle, we will get high probability of detecting a neutron at some places and high probability of proton, electron and neutrino at other places.

Even more, if we did a double-slit experiment with a neutron, we would get a sophisticated interference pattern of detecting neutrons, protons, electrons, neutrinos or no particle at all, with some probabilities. This would have to be huge experiment to let the neutron decay in the process. I make an assumption that 3 particles after neutron decay do not move relative to each other, which is not true in nature, but I hope you get the idea.

In general, any two entangled particles of any kind would give something like an interference pattern in the double-slit experiment.

That is really is interesting. Is that how you model radioactive particles? As the sum of the wave functions of the decay products?

Not quite. Rather, you can say that "physical" neutron is a sum of two waves: "ideal" neutron and (proton, electron, neutrino) triple. These 2 waves happen to be the mass states. Real physical neutron is not the mass state. If the decay products didn't interact except turning into a neutron again, and didn't scatter immediately after decay, then you would get something similar to neutrino oscillations.

Not quite. Rather, you can say that "physical" neutron is a sum of two waves: "ideal" neutron and (proton, electron, neutrino) triple. These 2 waves happen to be the mass states. Real physical neutron is not the mass state. If the decay products didn't interact except turning into a neutron again, and didn't scatter immediately after decay, then you would get something similar to neutrino oscillations.

What happens to the "ideal" neutron wave when the "physical" neutron decays?

We can kinda have interference pattern of different particles, at least in theory.

I don't understand that setup. Once the neutron decays, you have a proton and electron and neutrino propagating more or less freely. Before it decays you have none of these, and justa neutron propagating freely. Nothing is interfering with anything else.

Not quite. Rather, you can say that "physical" neutron is a sum of two waves: "ideal" neutron and (proton, electron, neutrino) triple. These 2 waves happen to be the mass states. Real physical neutron is not the mass state. If the decay products didn't interact except turning into a neutron again, and didn't scatter immediately after decay, then you would get something similar to neutrino oscillations.

I've never heard of this before and it sounds pretty iffy to me. Got a reference?

Even more, if we did a double-slit experiment with a neutron, we would get a sophisticated interference pattern of detecting neutrons, protons, electrons, neutrinos or no particle at all, with some probabilities. This would have to be huge experiment to let the neutron decay in the process. I make an assumption that 3 particles after neutron decay do not move relative to each other, which is not true in nature, but I hope you get the idea.

This doesn't really make sense to me. If you let the neutron decay you would get detections and interference of protons, electrons, and nuetrinos but no neutrons, as they have decayed. (Or rather most of them depending on the amount of time between emission and detection)